Question

how to you express cos4x in terms of sin

Answer 1

First find cos(2x).
cos(2x) = cos(x+x) = cosxcosx - sinxsinx
= cos^2x - sin^2x
=1-2sin^2(x)

Then cos(4x) =cos(2x+2x) = cos2xcos2x - sin2xsin2x
= (1-2sin^2x)(1-2sin^2x) - 2sinxcosx.2sinxcosx
= (1-4sin^2x +4sin^4x) -4sin^2xcos^2x
= 1-4sin^2x+4sin^4x -4sin^2x(1-sin^2x)
= 1-8sin^2(x)+8sin^4(x)

Answer 2

Thanks